“Foxcatcher” tells a strange, tragic, based-in-fact story about an eccentric multi-millionaire and the Olympic gold medal-winning brothers he tears apart.

Steve Carell, who gained famed through comic TV and film work prior to his recent dramatic roles, solemnly assumes the part of John Eleuthère du Pont, a man of privilege and member of a powerful American dynasty.

Carell is physically transformed for the role, largely through the prosthetic nose he wields like a beak. That nose and the often creepy demeanor Carell adopts as du Pont give the character a bird of prey stare.

In one instance of du Pont’s unsettling personality, he tells Mark Schultz, an Olympic wrestler he recruits to a state-of-the-art training facility at the du Pont family’s Foxcatcher Farms estate, not to refer to him as Mr. du Pont. He prefers to be called the Eagle, Golden Eagle or John.

The self-glorifying du Pont imagines himself to be a mentor, coach and father figure. His grandiosity would be amusing if it weren’t so twisted. Carell, the comic, uses his deadpan skills to chilling effect. His tour de force performance as du Pont is nearly a horror show.

In Schultz, wrestling fan du Pont finds a young champion to play mentor to. Channing Tatum goes to dark psychological places as Schultz. Like du Pont, it’s an often scary performance, but Schultz usually only hurts himself. This brave work by Tatum is the most soul-scraping performance of the actor’s life.

Mark Ruffalo plays the third person in the film’s tragic trio. According to the thorny sibling portrait in “Foxcatcher,” Dave Schultz has been protector, teacher and proxy parent for his younger brother Mark throughout their lives. It seems that Mark would be lost without the loving, understanding Dave.

The step-above “Foxcatcher” performances continue with Ruffalo’s Dave. The actor plays the elder Schultz with palpable warmth. He’s the sibling anyone would want. Like Carell, too, Ruffalo is physically transformed for role and, at least at first sight, unrecognizable.

Mark Schultz and du Pont are a volatile combination. Away from his brother’s guidance, Mark accepts du Pont as a friend, which opens the door to him being led astray. Already deeply insecure, Mark is a fox outgunned.

“Foxcatcher” very much has the mark of its director, Bennett Miller. The film’s tone recalls the quietly dramatic storytelling seen in 2005’s “Capote,” another story that deftly combines biopic elements with specific events framed in a precise period of time. Like the painters of the portraits of du Pont’s industrial kingpin ancestors that hang in the family’s mansion on a Pennsylvania hillside, Miller, screenwriters E. Max Frye and Dan Futterman and their cast — including Vanessa Redgrave as du Pont’s disapproving mother, Jean — tell the story in meticulously applied, character-revealing strokes.

The interplay between the Schultz brothers and du Pont, especially, is plotted in masterful style. Carell’s leering du Pont, a sad, damaged soul who’s blind to his princely vanity, becomes, in the character’s stealthy way, an unforgettable villain.